First things first - is there tiling/waterproof panelling from bath to ceiling? If not you will damage the walls and plaster by putting a shower in without tiles or panels to protect the walls.
You can get attachments that fit onto bath taps and screw a holder onto the wall so you can shower without holding the attachment easily enough - good if you are on a budget or just need a temporary solution quickly. I would look at changing the taps to a set with a shower attachment or installing a thermostatic shower as a longer term solution.
For speed, you can buy telescopic shower rails to hang a shower curtain from - measure the space before you buy one - they don't need to be screwed into place.
Specialsubject makes a very good point there. One I hadn't thought of. A friend of mine ruined her bathroom wall by using a shower in a space that was only half tiled. She was lucky it was just the wall too.
If you do have any doubts, don't do it yourself - get a plumber to take a look and advise on what needs doing.
Also check that the tiling is sound and none of the tiles is loose - if you do find a loose one it is pretty easy to fix yourself, there are tutorials on Youtube.
cautionary tale - we had a fully tiled bathroom until one day they started falling off, accelerating the planned renovation. Only then did we look under the bath, to find cracked chipboard that had been wet...
no idea how someone didn't end up going through the ceiling, not to mention with tiles on their head as they were really badly fixed.
FWIW bath fitting hints; support the legs on solid wood, then have more wood resting on bricks and fill the space with expanding foam to support the whole bath. For the sealant, fill the bath, then seal, and leave for 24 hours before emptying the bath and using.
oh, and consider shower panels - no grout to go mouldy, quite easy to fit and look good.